The article sparked a rebuttal of Michael Avenatti, a lawyer for Stormy Daniels, on Twitter.
Tweeted, "Mr. Cohen should make sure that he makes the REIMBURSABLE bookings for the extended vacation he's planning for my clients' money … …"
Avenatti told CNN last week that Daniels "was physically threatened for keeping silent about what he knew about Donald Trump," and said his client would provide more details in a "60 Minutes" interview without air.
Cohen told Vanity Fair that he did not threaten Daniels and that he had never spoken to her, but interacted with her through a previous lawyer.
"I can only speak for myself," he said when asked about the alleged threat. "I reiterate: I have never threatened her in any way, and I am not aware of anyone else doing it"
Avenatti told CNN in response that "there is no doubt at this point that Mr. Cohen's credibility is very suspicious. "
Cohen previously stated that his action was legal, and in the Vanity Fair article, he is quoted as saying that his decision was not related to the Trump campaign.
"People are confusing this for something about the campaign," Cohen said. "What I did defensively for my personal client, and my friend, is what lawyers do for their high profile clients, I would have done it in 2006. I would have done it in 2011. I really care about him and his family: – More than just as an employee and lawyer. "
Sara Sidner of CNN contributed to this report.